update: Feb. 21, 2014
 ABSTRACT
- Nao Imoto (M2, Nara Women's University)
On Alexander invariant of rational homology fibered knot
In this talk, we define a class of knots which is called
rational homology fibered knot by using rational homology, and study
Alexander invariants of them. We further define the monodromies of
ratioanal homology fiber surfaces, and see how they are related to
the Alexander invariants. We also see that there is a decomposition
of monodromy corresponding to mutually disjoint, rational homology
fiber surfaces for a knot. We show some examples of such decomposition
of monodromy.
- Sukuse Abe (D1, Saitama University)
Definition of finite type invariants of connected oriented
compact 3-manifolds, and Qundle homotopy (cocycle) invariants
We obtain a finite type invariant of connected oriented compact 3-manifolds.
The domain of 3-manifolds is larger than the integral homology 3-spheres of
LMO invariant.
However, this invariant induces the homology of 3-manifold,
and we give a filtration to the domain of mapping class groups.
- Kodai Wada (M1, Tokyo Gakugei University)
Covering linkage invariants of Brunnian links and their Milnor invariants
[a joint work with Kodai Wada (M1, Tokyo Gakugei University)]
Let L be an (n+1)-component Brunnian link in 3-sphere
$S^3$ and K a component of L. Then the double branched cover of $S^3$
branched over K is still $S^3$.
In particular each lift of $L \setminus K$ is an n-component Brunnian link.
We show that the Milnor invariants of length n+1 for the link L is
modulo-2 congruent to a sum of Milnor invariants of length n for lifts of
$L \setminus K$. (This is a joint work with Natsuka Kobayashi.)
- Sachiko Ohtani (National Defense Academy of Japan)
Arithmetic topology for moduli of Galois representations
Arithmetic topology is a study that views $3$-dimensional topology
and algebraic number theory as analogies from the viewpoint
of group theory and Galois theory, which have appeared recently
in the classification of mathematics.
That fundamental concept is based on analogies between
knots and prime numbers. In this talk, we discuss an analogy
between moduli of representations of knot groups and Galois groups.
- Yuki Temma (M1, Nihon University)
Non-left-orderable surgeries and presentations of knot groups
I will talk about non-left-orderable surgeries on knots.
A Dehn surgery is called a non-left-orderable surgery if it yields a closed
3-manifold with non-left-orderable fundamental group. I found presentations
of knot groups which make possible to have a non-left-orderable surgery for
a given knot in the 3-sphere.
This result gives an extention of Nakae's result.
- Shinya Okazaki (OCAMI, Osaka City University)
Bridge genus and braid genus for 3-manifolds
The bridge genus and the braid genus are invariants of a closed connected
orientable 3-manifold M which are introduced by A. Kawauchi.
The bridge genus $g_{\scriptsize\rm{bridge}}(M)$
(resp. the braid genus $g_{\scriptsize\rm{braid}}(M))$ of M is the
minimal number of bridge(L)
(resp. braid(L)) for any L such that M is obtained by the
0-surgery of S^3 along a link L.
In this talk, we calculate the bridge genus and braid genus for some
3-manifolds.
- Hideo Takioka (D2, Osaka City University)
The $\Gamma$-polynomial of a knot and its applications
The $\Gamma$-polynomial is an invariant of an oriented link in
the 3-sphere, which is contained in both the HOMFLYPT and Kauffman
polynomials as their common zeroth coefficient polynomial.
As applications of the $\Gamma$-polynomial,
I will talk about the following topics:
- On the arc index of cable knots (joint with Hwa Jeong Lee, KAIST)
- On the braid index of Kanenobu knots
- On the arc index of Kanenobu knots (joint with Hwa Jeong Lee, KAIST)
- On the cable $\Gamma$-polynomials of mutant knots
- Jean-Baptiste Meilhan（Institut Fourier, Universite Grenoble I）
Homotopy classification of welded and ribbon 2-string links
"Ribbon 2-knotted surfaces" are locally flat embeddings of surfaces
in 4-space which bound immersed 3-manifolds with only ribbon singularities.
These objects also appear as topological realizations of "welded
knotted objects", which is a natural quotient of virtual knot theory.
In this talk, we consider ribbon tubes, which are knotted annuli
bounding ribbon 3-balls.
We will see how ribbon tubes naturally act on the reduced free group,
and that this action
classifies ribbon tubes up to homotopy, that is, when allowing each
tube component to cross itself.
At the combinatorial level, this provides a classification of
welded string links up to self-virtualization, and the above-mentionned action
on the reduced free group can be seen as the "virtual extension" of Milnor invariants.
This generalizes a result of Habegger and Lin on string links.
This talk is based on a joint work with B. Audoux, P. Bellingeri and E. Wagner.
It is addressed to non-specialists, an will in particular review all
the background notions for the results.
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